ORDER AND JUDGMENT*
STEPHEN H. ANDERSON, Circuit Judge.Plaintiffs John Hadley Fisher and Kenneth Lynn Funkhouser, Oklahoma state inmates proceeding pro se here as in the district court, appeal the district court’s order granting summary judgment to defendants on their claims arising under 42 U.S.C. § 1983. We exercise jurisdiction under 28 U.S.C. § 1291 and affirm.
*707 Background,
Each plaintiff is serving a life sentence for murder. Both are incarcerated at the Oklahoma State Prison (OSP), and were housed at H Unit during the relevant time. Mr. Funkhouser wrote a letter to an OSP staff case manager, and Mr. Fisher wrote at least two letters to her. Plaintiffs assert that defendants circulated the letters among the inmates in their housing unit, resulting in both plaintiffs being labeled as informants or snitches.
Plaintiffs filed the underlying lawsuit alleging that defendants violated their constitutional rights by labeling them as snitches with the intent that they be injured or killed. Plaintiffs requested appointment of counsel, discovery, and a preliminary injunction. At the district court’s direction, defendants filed a Martinez report.1 Plaintiffs later sought to supplement their pleadings to include allegations that defendants retaliated against them for filing suit. The district court granted defendants’ motion for summary judgment and denied all other pending motions. Plaintiffs appeal, arguing (1) the district court’s entry of summary judgment was improper because discovery had not been allowed and there existed disputed facts, (2) the district court abused its discretion in denying their motions for appointment of counsel, for an injunction, and to supplement their pleadings, (3) the district court erred in denying their claims under the Eighth Amendment, and (4) the district court erred in denying Mr. Funkhouser’s claims under the Fifth, Eighth, and Fourteenth Amendments and the Equal Protection Clause.
Standards of Review
“We review the grant of summary judgment de novo, applying the same standard the district court should apply under Fed. R.Civ.P. 56(c).” Steffey v. Orman, 461 F.3d 1218, 1221 (10th Cir.2006) (quotation omitted). For dispositive issues on which the plaintiff will bear the burden of proof at trial, he must “go beyond the pleadings and designate specific facts so as to make a showing sufficient to establish the existence of an element essential to [his] case in order to survive summary judgment.” Sealock v. Colorado, 218 F.3d 1205, 1209 (10th Cir.2000) (quotation omitted). “[E]vidence, including testimony, must be based on more than mere speculation, conjecture, or surmise. Unsubstantiated allegations carry no probative weight in summary judgment proceedings.” Self v. Crum, 439 F.3d 1227, 1230 (10th Cir.) (citation and quotations omitted), cert. denied, — U.S. -, 127 S.Ct. 131, 166 L.Ed.2d 96 (2006).
We review a district court’s discovery rulings, its order denying leave to supplement the pleadings, and its order denying appointment of counsel for an abuse of discretion. Procter & Gamble Co. v. Haugen, 427 F.3d 727, 742-43 (10th Cir.2005) (discovery); Walker v. United Parcel Serv., Inc., 240 F.3d 1268, 1278 (10th Cir. 2001) (leave to supplement); Steffey, 461 F.3d at 1223 (appointment of counsel). An order denying a preliminary injunction will not be disturbed absent an abuse of discretion, an error of law, or clearly erroneous factual findings. Kikumura v. Hurley, 242 F.3d 950, 955 (10th Cir.2001). Because plaintiffs are representing themselves, we liberally construe their pleadings; however, we do not act as their *708advocate. Hall v. Bellmon, 935 F.2d 1106, 1110 (10th Cir.1991).
Characterizing Plaintiffs as Informants
“A prison official’s deliberate indifference to a substantial risk of serious harm to an inmate violates the Eighth Amendment.” Farmer v. Brennan, 511 U.S. 825, 828, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994) (quotation omitted). “[L]abeling an inmate a snitch satisfies the Farmer standard, and constitutes deliberate indifference to the safety of that inmate.” Benefield v. McDowall, 241 F.3d 1267, 1271 (10th Cir.2001) (citing Northington v. Marin, 102 F.3d 1564, 1567 (10th Cir.1996)). But a prisoner must do more than allege generally that various prison officials violated his rights. “Rather, personal participation is an essential allegation in a § 1983 claim.” Mitchell v. Maynard, 80 F.3d 1433, 1441 (10th Cir.1996) (quotation omitted). In addition, “government officials are not vicariously liable for the misconduct of their subordinates. There is no concept of strict supervisor liability under § 1983.” Serna v. Colorado Dep’t of Corr., 455 F.3d 1146, 1151 (10th Cir.2006) (quotation omitted).
In their amended complaint, plaintiffs alleged that their letters were circulated by certain unknown prison employees and that the named defendants, with the exception of defendant Yott, were “culpable for [their] employees!’] actions.” R. Vol. I, Doc. 22 at 13. Defendants are not vicariously hable. Moreover, plaintiffs proffered no allegation or evidence that any of the named defendants, except Mr. Yott, personally participated in activities that violated their constitutional rights.2
Plaintiffs submitted sworn statements from nine fellow residents of H Unit purporting to substantiate their claims. Id. Doc. 24, Affidavits 11-17, 19 & 20. In the affidavits, the inmates stated that they had heard about plaintiffs’ letters or that it was common knowledge that plaintiffs had written to the case manager. Some of the affiants had read the letters, which they had received from other inmates or unidentified sources. Although several affiants stated that the letters were disseminated through the prison’s internal mail system, this was merely speculation; none of the affiants had personal knowledge of how the letters were revealed. We determine that the affidavits are insufficient to withstand summary judgment because they are based on either hearsay or speculation or both, and are therefore inadmissible. See Treff v. Galetka, 74 F.3d 191, 195 (10th Cir.1996) (holding content and substance of evidence opposing summary judgment must be admissible, and “inadmissible hearsay evidence in an affidavit will not defeat summary judgment”). Accordingly, plaintiffs’ claims that defendants (except Mr. Yott) violated their Eighth Amendment rights for labeling them snitches were properly denied.
As to Mr. Yott, plaintiffs alleged that he read their letters to two dangerous inmates. R. Vol. I, Doc. 22 at 5-6, 8-9. Mr. Yott stated in his affidavit that he investigated the claims made in plaintiffs’ letters and, in doing so, he discussed the letters with the two inmates because they were named in them. R. Vol. II, Doc. 28, Attach. 24 at 2-3. Plaintiffs’ allegations that Mr. Yott read their letters to the other *709inmates intending that those inmates would injure plaintiffs are conclusory. As such, they “are insufficient to put a material fact in dispute.” Ledoux v. Davies, 961 F.2d 1536, 1537 (10th Cir.1992). Plaintiffs have submitted no evidence that Mr. Yott acted with the requisite “obdurate and wanton disregard for [plaintiffs’] safety,” Northington v. Jackson, 973 F.2d 1518, 1525 (10th Cir.1992). Therefore, the district court properly granted summary in favor of Mr. Yott on this claim.
Remaining Claims of Both Plaintiffs
Plaintiffs maintain that the district court erred in entering summary judgment before they had conducted discovery. Their primary complaint concerns their request for DNA testing on the envelopes containing their letters that were sent to other inmates, which they assert would have revealed the identity of the sender or senders. As discussed above, plaintiffs’ amended complaint alleged that almost all of the actionable conduct was done by unknown persons. We recognize that plaintiffs had hoped discovery would help them identify one or more prison employees they could sue, but under these circumstances where the letters could have been disseminated by any number of people, including inmates, we find no abuse of discretion' in the district court’s decision foreclosing plaintiffs’ attempt to “use discovery as a fishing expedition,” Anthony v. United States, 667 F.2d 870, 880 (10th Cir.1981).
Plaintiffs next argue that the district court misconstrued their claims for damages, incorrectly holding that they requested, but were not entitled to, damages for psychological injury. The district court held correctly that plaintiffs may not recover for emotional injury absent physical injury. See 42 U.S.C. § 1997e(e). Although § 1997e(e) does not bar recovery of nominal or punitive damages, Searles v. Van Bebber, 251 F.3d 869, 879, 880-81 (10th Cir.2001), plaintiffs are not entitled to any damage award, given the district court’s entry of summary judgment in defendants’ favor and our affirmance.
Similarly, we find no abuse of discretion in the district court’s order denying appointment of counsel. Having reviewed the record and the briefs, we conclude that plaintiffs’ case is not one of “those extreme cases where the lack of counsel resulted] in fundamental unfairness,” Steffey, 461 F.3d at 1223 (quotation omitted).
Plaintiffs also assert that the district court erred in denying their request for a preliminary injunction. They sought to enjoin the defendants from transferring them to another prison, seizing their legal materials, interfering with their ability to confer with each other, and generally retaliating against them for filing this action. R. Doc. 39, Attach. We conclude that plaintiffs have not made any of the required showings — that they- are likely to succeed on a retaliation claim, that they will suffer irreparable injury if an injunction is not issued, that the threatened injury to them outweighs any injury to defendants, or that an injunction would not be averse to the public interest. See Kikumura, 242 F.3d at 955. Therefore, we affirm the district court’s denial of a preliminary injunction.
Plaintiffs further challenge the district court’s decision not to allow them to supplement their pleadings. It appears that the requested supplement sought to add a new claim that defendants retaliated against plaintiffs for filing suit. Under Fed.R.Civ.P. 15(d), “trial courts [have] broad discretion to permit a party to serve a supplemental pleading setting forth post-complaint transactions, occurrences or events.” Walker, 240 F.3d at 1278. But at *710the time the motion to supplement was filed, the case was ready for disposition on summary judgment on the original claims. Under these circumstances, we conclude that the district court did not abuse its discretion in denying leave to supplement the pleadings. See id.
Plaintiff Funkhouser’s Remaining Claims
Mr. Funkhouser asserts that defendants’ consideration of his conduct during a riot at the prison in 1985 was improper because he was acquitted of the criminal charges brought against him. He maintains that defendants violated his constitutional rights by placing him in H Unit and keeping him there based on his participation in the riot. According to Mr. Funkhouser, H Unit was also known as “Redline,” and was used unofficially to punish and coerce him and other prisoners by keeping them in unconstitutionally harsh conditions of confinement.
Mr. Funkhouser contends that his transfer to H Unit based on his participation in the riot was a double-jeopardy violation because he was acquitted of the criminal charges. Prison classification does not implicate that Fifth Amendment right. Cf. Wirsching v. Colorado, 360 F.3d 1191, 1205 (10th Cir.2004) (holding double jeopardy not implicated in prison disciplinary sanctions).
Next, Mr. Funkhouser argues that his transfer to H Unit was punitive, and therefore he was entitled to Fourteenth-Amendment due-process procedures before and during his placement there. He alleges that the conditions in H Unit were similar to those in the administrative segregation unit, whereby prisoners were denied contact visits, a yard permitting contact with other inmates, jobs, and programs. He also claims that the conditions in H Unit imposed atypical and significant hardship in comparison to other cell blocks at OSP.
In his affidavit, the warden stated that (1) OSP provided housing primarily for maximum-security offenders, (2) all inmates were afforded very limited outdoor exercise, (3) H Unit, Northwest 1, where Mr. Funkhouser was housed, was a general-population unit, (4) non-contact visiting was imposed on all inmates in all cell blocks of H Unit, as well as to inmates classified as level one and those in Units D and E, and (5) work assignments were, available on a very limited basis and were assigned based on conduct, attitude and an ability to cooperate. R. Vol. II, Doc. 28, Attach. 22 at 1-3.
The Supreme Court has held that States may under certain circumstances create liberty interests which are protected by the Due Process Clause. But these interests will be generally limited to freedom from restraint which, while not exceeding the sentence in such an unexpected manner as to give rise to protection by the Due Process Clause of its own force, nonetheless imposes atypical and significant hardship on the inmate in relation to the ordinary incidents of prison life.
Sandin v. Conner, 515 U.S. 472, 483-84, 115 S.Ct. 2293, 132 L.Ed.2d 418 (1995) (citations omitted). Defendants do not dispute Mr. Funkhouser’s claims about the conditions in H Unit. In fact, they confirm those claims. Mr. Funkhouser did not produce facts showing that H Unit’s conditions were harsher, or even different, than those in other comparable units in the maximum-security prison. Therefore, he was not entitled to due process before or during his placement at H Unit.
Finally, Mr. Funkhouser asserts that his equal protection rights were violated when he was transferred to and re*711tained at H Unit, while other prisoners with worse institutional records were not. He argues on appeal that defendants’ responses to his discovery requests would have established that other prisoners were treated more favorably than he.
“Equal protection is essentially a direction that all persons similarly situated should be treated alike.” Fogle v. Pierson, 435 F.3d 1252, 1260 (10th Cir.) (quotation omitted), cert. denied, — U.S.-, 127 S.Ct. 675, 166 L.Ed.2d 526 (2006). Mr. Funkhouser does not claim that he was treated differently than other inmates because he belongs to a suspect class; therefore, he must show that he was similarly situated to the other inmates “and that the difference in treatment was not ‘reasonably related to legitimate penological interests.’ ” Id. at 1261 (quoting Turner v. Safley, 482 U.S. 78, 89, 107 S.Ct. 2254, 96 L.Ed.2d 64 (1987)).
The placement of prisoners within OSP is in part discretionary. See Okla. Stat. tit. 57, § 138(D); see also Wilson v. Jones, 430 F.3d 1113, 1116 (10th Cir.2005) (describing Oklahoma’s statutory classification system as having both objective and subjective/discretionary components), cert. denied, — U.S.-, 127 S.Ct. 158, 166 L.Ed.2d 253 (2006). The numerous subjective factors contributing to the classification of prisoners demonstrates the implausibility of Mr. Funkhouser’s argument that “there are no relevant differences between [him] and other inmates that reasonably might account for their different treatment.” Fogle, 435 F.3d at 1261 (quotation omitted). For the same reason, the discovery Mr. Funkhouser would have requested about other prisoners’ institutional records would not have proven his equal protection claim. Consequently, the district court properly rejected the equal protection claim without allowing discovery.
Conclusion
Plaintiffs’ pending motions are DENIED. The judgment of the district court is AFFIRMED.
After examining the briefs and appellate record, this panel has determined unanimously that oral argument would not materially assist the determination of this appeal. See Fed. R.App. P. 34(a)(2); 10th Cir. R. 34.1(G). The case is therefore ordered submitted without oral argument. This order and judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. It may be cited, however, for its persuasive value consistent with Fed. R.App. P. 32.1 and 10th Cir. R. 32.1.
. Martinez v. Aaron, 570 F.2d 317 (10th Cir. 1978) (per curiam) (approving order requiring prison officials to investigate facts surrounding inmate’s civil rights action to construct an administrative record from which court may determine jurisdiction and assess frivolity).
. Although courts generally permit a plaintiff to use unnamed defendants, the plaintiff must “provide!] an adequate description of some kind which is sufficient to identify the person involved so process eventually can be served.” Roper v. Grayson, 81 F.3d 124, 126 (10th Cir.1996). Here, plaintiffs’ amended complaint did not describe the person or persons they claim injured them. Accordingly, the district court did not err in entering summary judgment.